A stiff brush should be all you need. The intense oven heat should burn up anything stuck to the oven floor. Any liquid on the stone while it is still hot risk cracking the stone. Those take a good 4+ hours to cool if I am not mistaken.
The better question is figuring out how to keep it clean/er.
The deck ovens I used at a hotel I baked bread in were absolutely destroyed. The bakers, before i showed up and took over oven duties would either forget to steam, or try to steam before the oven steam was 'recharged' and resorted to tossing in quarts of water. Cracks everywhere.